This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A253175 #27 May 30 2025 10:10:26
%S A253175 1,7,67,661,6541,64747,640927,6344521,62804281,621698287,6154178587,
%T A253175 60920087581,603046697221,5969546884627,59092422149047,
%U A253175 584954674605841,5790454323909361,57319588564487767,567405431320968307,5616734724645195301,55599941815130984701
%N A253175 Indices of hexagonal numbers (A000384) which are also centered hexagonal numbers (A003215).
%C A253175 Also positive integers x in the solutions to 4*x^2-6*y^2-2*x+6*y-2 = 0, the corresponding values of y being A253475.
%H A253175 Colin Barker, <a href="/A253175/b253175.txt">Table of n, a(n) for n = 1..1000</a>
%H A253175 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-11,1).
%F A253175 a(n) = 11*a(n-1)-11*a(n-2)+a(n-3).
%F A253175 G.f.: -x*(x^2-4*x+1) / ((x-1)*(x^2-10*x+1)).
%F A253175 a(n) = (2+(5-2*sqrt(6))^n*(3+sqrt(6))-(-3+sqrt(6))*(5+2*sqrt(6))^n)/8. - _Colin Barker_, Mar 05 2016
%F A253175 4*a(n) = 1+3*A072256(n). - _R. J. Mathar_, Feb 07 2022
%F A253175 a(n) = A350923(n)/2. - _Paolo Xausa_, May 30 2025
%e A253175 7 is in the sequence because the 7th hexagonal number is 91, which is also the 6th centered hexagonal number.
%t A253175 LinearRecurrence[{11, -11, 1}, {1, 7, 67}, 25] (* _Paolo Xausa_, May 30 2025 *)
%o A253175 (PARI) Vec(-x*(x^2-4*x+1)/((x-1)*(x^2-10*x+1)) + O(x^100))
%Y A253175 Cf. A000384, A003215, A253475, A006244, A350923.
%K A253175 nonn,easy
%O A253175 1,2
%A A253175 _Colin Barker_, Jan 08 2015